engleski

Variabilty response function for stochastic thin plate bending problem

The concept of variability response function based on the weighted integral method and the local averaging method is extended to thin plate bending problem. The elastic modulus of the structure is considered to be two-dimensional, homogenous, stochastic field. The stochastic stiffness matrix is calculated by using Hermitian bicubic finite element. The stochastic element stiffness matrix is represented as linear combination of deterministic element stiffness matrix and 37 random variables (weighted integrals) with zero-mean property. The concept of the variability response function is used to compute upper bounds of the response variability. The first and second moment of the stochastic elastic modulus are used as input quantities for description of the random variable. The response variability is calculated using first-order Taylor expansion approximation of the variability response function. The use of the variability response function based on the weighted integral method is compared with the use of a variability response function based on the local averaging method in the sence to show the influence of the reducing the computational effort on the loss of the accuracy. The using of local averaging method gives approximation with small loss of accuracy with only one random variable per each finite element. Numerical examples are provided for both methods and for different boundary and loading conditions, different wave numbers and different number of the finite elements.

stochastic finite element; plate bending; weighted integrals; local-averaging method; response variability; spectral-distribution-free upper bounds

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